Q301JEE Main 2019MCQ

A rigid diatomic ideal gas undergoes anadiabatic process at room temperature,. Therelation between temperature and volume ofthis process is $TV^x$ = constant, then x is :

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📖 Explanation

For adiabatic process : $TV^{\gamma -1}$ = constantFor diatomic process : γ - 1 = $7/5-1$ ∴ x = $2/5$

Q302JEE Main 2019MCQ

A metal ball of mass 0.1 kg is heated upto 500°C and dropped into a vessel of heat capacity 800 $JK^{-1}$ and containing 0.5 kg water. The initial temperature of water and vessel is 30°C. What is the approximate percentage increment in the temperature of thewater ? $[Specific Heat Capacities of water and metal are, respectively, 4200 $Jkg^{-1}K^{-1}$ and 400 $JKg^{-1}K^{-1}$ ]$

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📖 Explanation

0.1 × 400 × (500 - T) = 0.5 × 4200 × (T - 30)+ 800 (T - 30) ⇒ 40(500 - T) = (T - 30) (2100 + 800) ⇒ 20000 - 40T = 2900 T - 30 × 2900 ⇒ 20000 + 30 × 2900 = T(2940) T = 30.4°C ${\Delta T}/T$ × 100 = $\frac{6.4}{30}$ × 100 = 20%

Q303JEE Main 2019MCQ

A Carnot engine has an efficiency of $1/6$ . When by $62° C$ , its efficiency is doubled. The temperature of the source and the sink are, respectively,

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📖 Explanation

$\ η=1-\ \frac{T_{2}}{T_{1}}$ $\ \frac{1}{6}=1-\ \frac{T_{2}}{T_{1}} \Rightarrow \frac{T_{2}}{T_{1}}=1-\ \frac{1}{6}=\ \frac{5}{6}$ $2 \ η=1-\ (\ \frac{T_{2}-62}{T_{1}} )$ $2 \\times \ \frac{1}{6}+\ \frac{62}{T_{1}} \Rightarrow T_{1}=62 \times 6 T_{1}=372 K$ $T_{1}=372-273=99^{\°} C$ $T_{2}=\ \frac{5}{6}\times 372=310 K$ $T_{2}=310-273=37^{\°} C$

Q304JEE Main 2019MCQ

Ice at -20° C os added tp 50 g of water at 40°C. When the temperature of the mixture reaches 0°C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/°C) Specific heat of Ice = 2.1 J/g/°C Heat of fusion of water at 0°C = 334 J/g)

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Q305JEE Main 2019MCQ

A sample of an ideal gas is taken through the cyclic process abca as shown in the figure. The change in the internal energy of the gas along the path ca is -180 J. The gas absorbs 250 J of heat along the path ab and 60 J along the path bc. The work done by the gas along the path abc is.

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📖 Explanation

$d Q=d U+d W$ $250+60=180+d W$ $d W=130 J$

Q306JEE Main 2019MCQ

An HCl molecule has rotational, translational and vibrational motions. If the rms velocity of HCl molecules in its gaseous phase is $v ^{\to }$ , m is its mass and $k_B$ is Boltzman constant, then its temperature will be :

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📖 Explanation

According to equipartion energy theorem $\;\frac{1}{2} m(v_{r m s}^{2})=3 \times \;\frac{1}{2} K_{b} T$ $\;T=\;\frac{m v_{r m s}^{2}}{3 k}=\;\frac{m \overline{v}^{2}}{3 k_{B}}$

Q307JEE Main 2019MCQ

An unknown metal of mass 192 g heated to a temperature of 100°C was immersed into a brass calorimeter of mass 128 g containing 240 g of water a temperature of 8.4°C Calculate the specific heat of the unknown metal if water temperature stabilizes at 21.5°C(Specific heat of brass is 394 J $kg^{-1} K^{-1}$ )

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Q308JEE Main 2019MCQ

A cylinder with fixed capacity of 67.2lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is : $[Given that R=8.31J $\text{mol}^{-1} \text{k}^{-1}$ ]$

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📖 Explanation

$\Delta Q=n C_{v} \;\; \Delta T=n \;\frac{3}{2} R \Delta T$ $=(\;\frac{67.2}{22.4})(\;\frac{3}{2} \times 8.31)(20)$ $\approx 748 {J}$

Q309JEE Main 2019MCQ

A massless spring(k = 800 N/m), attached with a mass (500g) is completely immersed in 1 kg of water. The spring is stretched by 2cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely? (Assume that the water container and spring receive negligible heat and specific heat of mass = 400 J/kg K, specific heat of water = 4148J /kg K) A.

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📖 Explanation

Finally, the block comes to its equilibrium position, where $K x_{e q}=m g-v e g$ $800\ (x_{e q}\ )=(0.5)(10)-v e g$ Energy lost by body due to oscillatins $= \frac{1}{2} K\ (x_{e q}+x\ )^{2}-\ \frac{1}{2} K (x_{m} )^{2}-(m g-v e g)$ $=\ \frac{1}{2} K\ (x^{2}\ )+\ (k x_{e q}-m g+(0) v e g\ ) x$ $=\ \frac{1}{2} k x^{2}=\ \frac{1}{2}(800)(0.02)^{2}$ $=400 \times 4 \\times 10^{-4}$ $=0.16 J$ This is equal to the heat transferred $0.16 J=(0.5)(400)(\Delta T)+(1)(4184)(\Delta T)$ $0.16=(4384) \Delta T$ . $\Delta T=\ \frac{16}{4.384} \\times \frac{10^{-2}}{10^{3}}$ $\therefore$ It is of the order of $10^{-5}$

Q310JEE Main 2019MCQ

A diatomic gas with rigid molecules does 10 J of work when expanded at constant pressure. When would be the heat energy absorbed by the gas, in this process?

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📖 Explanation

$\ d Q_{P} =n C_{P} d T,\; \gamma =7 / 5$ $\frac{d w}{d Q_{p}} =1-\ \frac{1}{\gamma }=1- \frac{5}{7}=\ \frac{2}{7}$ $d Q_{P}=\ \frac{7}{2} \times 10=35 \ {J}$

Q311JEE Main 2019MCQ

When 100 g of a liquid A at 100°C is added to 50 g of a liquid B at temperature 75°C, the temperature of the mixture becomes 90°C. The temperature of the mixture, if 100 g of liquid A at 100°C is added to 50 g of liquid B at 50°C, will be :-

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📖 Explanation

100 × $S_A$ × [100 - 90] = 50 × $S_B$ × (90 - 75) $2S_A$ = 1.5 $S_B$ $S_A$ = $3/4 S_B$ Now, 100 × $S_A$ × [100 - T] = 50 × $S_B$ (T - 50) 2 × $(3/4)$ (100 - T) = (T - 50) 300 - 3T = 2T - 100 400 = 5T T = 80

Q312JEE Main 2019MCQ

A gas can be taken from A to B via two differentprocesses ACB and ADB When path ACB is used 60 J of heat flows into thesystem and 30 J of work is done by the system. Ifpath ADB is used work done by the system is 10J. The heat Flow into the system in path ADB is : [9-Jan-2019 Shift 1]

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📖 Explanation

Δ $Q_{ACB}$ = Δ $W_{ACB}+\Delta U_{ACB}$ \Rightarrow 60 J = 30 J + Δ $U_{ACB}$ \Rightarrow Δ $U_{ACB}$ = 30 J \Rightarrow Δ $U_{ADB}$ = Δ $U_{ACB}$ = 30 J Δ $Q_{ACD}$ = Δ $U_{ACB}+\Delta W_{ADB}$ = 10 J + 30 J = 40 J

Q313JEE Main 2019MCQ

Two Carrnot engines A and B are operated in series. The first one, A, receives heat at $T_1$ (= 600 K) and rejects to a reservoir at temperature $T_2$ . The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at $T_3$ (= 400 K). Calculate the temperature $T_2$ if the work outputs of the two engines are equal :

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📖 Explanation

$w_1$ = $w_2$ Δ $u_1$ = Δ $u_2$ $T_3-T_2$ = $T_2-T_1$ 2 $T_2$ = $T_1+T_3$ $t_2$ = 500 K

Q314JEE Main 2019MCQ

Two rods A and B of identical dimensions areat temperature 30°C. If A is heated upto 180°Cand B upto T°C, then the new lengths are thesame. If the ratio of the coefficients of linearexpansion of A and B is 4 : 3, then the valueof T is :-

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📖 Explanation

Δ $l_1$ = Δ $l_2$ l $\alpha _1\Delta T_1$ = l $\alpha _2\Delta T_2$ $\alpha _1/\alpha _2$ = $\frac{\Delta T_1}{\Delta T_2}$ $4/3$ = $\frac{T-30}{180-30}$ T = 230° C

Q315JEE Main 2019MCQ

The given diagram shows four processes i.e., isochoric, isobaric, isothermal and adiabatic. The correct assignment of the processes, in the same order is given by:

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📖 Explanation

$P V^{n}=$ constant If $n=0,$ isobaric $n=1$ isothermal $n=\gamma$ adiabatic $n=\infty$ isochoric

Q316JEE Main 2019MCQ

A vertical closed cylinder is separated into two parts by a frictionless piston of mass m and of negligible thickness. The piston is free to move along the length of the cylinder. The length of the cylinder above the piston is $l_1$ , and that below the pistonis $l_2$ , such that $l_1$ > $l_2$ . Each part of the cylinder contains n moles of an ideal gas at equal temperature T. If the piston is stationary, its mass, m, will be given by : (R is universal gas constant and g is the acceleration due to gravity)

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📖 Explanation

$P_2A$ = $P_1A$ + mg $\frac{nRT.A}{Al_2}$ = $\frac{nRT.A}{Al_1}$ + mg nRT $(1/l_2-1/l_1)$ = mg m = ${nRT}/g$ $(\frac{l_1-l_2}{l_1 . l_2})$

Q317JEE Main 2018MCQ

Two moles of an ideal monoatomic gas occupies a volume V at 27°C . The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b)change in its internal energy.[Main 8 April 2018]

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📖 Explanation

$Tv^{\gamma -1}=const$ $300v^{2/3}=T.2^{2/3}v^{2/3}$ $T=300/2^{2/3}=189K$ $\Delta u=nc_v\Delta T$ $=-2.7KJ$

Q318JEE Main 2018MCQ

Two cornot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature $T$ . Engine $B$ receives heat rejected by engine $A$ and in turn rejects it to a reservoir at 100 K . If the efficiencies of the two engines $A$ and $B$ are represented by $η_A$ and $η_B$ , respectively, then what is the value of $\;\frac{η_B}{η_A}$ ?

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Q319JEE Main 2018MCQ

One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :[Main 16 April 2018 S1]

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Q320JEE Main 2018MCQ

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature,27°C. The work done on the gas will be :[Main 15 April 2018 S1]

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