Initial pressure and volume of a gas are P and V respectively. First it is expanded isothermally to volume 4V and then compressed adiabatically to volume V. The final pressure of gas will be [Given : -

(1) 1P

(2) 2P

(3) 4P

(4) 8P

Concept Questions :-

Types of processes
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A thermally insulated rigid container contains an ideal gas heated by a filament of resistance 100 Ω through a current of 1A for 5 min . Then change in internal energy is -

(1) 0 kJ

(2) 10 kJ

(3) 20 kJ

(4) 30 kJ

Concept Questions :-

First law of thermodynamics
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A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62°C, the efficiency of the engine is doubled. The temperatures of the source and sink are -

(1) 80°C, 37°C

(2) 95°C, 28°C

(3) 90°C, 37°C

(4) 99°C, 37°C

Concept Questions :-

Heat engine and refrigerator
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An ideal gas expands in such a manner that its pressure and volume can be related by equation . During this process, the gas is

(1) Heated

(2) Cooled

(3) Neither heated nor cooled

(4) First heated and then cooled

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P-V diagram of a diatomic gas is a straight line passing through origin. The molar heat capacity of the gas in the process will be -

(1) 4 R

(2) 2.5 R

(3) 3 R

(4) $\frac{4R}{3}$

Concept Questions :-

Molar Specific heat
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Following figure shows on adiabatic cylindrical container of volume V0 divided by an adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal gas $\left({C}_{P}/{C}_{V}=\gamma \right)$ is at pressure P1 and temperature T1 in left part and gas at pressure P2 and temperature T2 in right part. The piston is slowly displaced and released at a position where it can stay in equilibrium. The final pressure of the two parts will be (Suppose x = displacement of the piston)

(1) P2

(2) P1

(3) $\frac{{P}_{1}{\left(\frac{{V}_{0}}{2}\right)}^{\gamma }}{{\left(\frac{{V}_{0}}{2}+Ax\right)}^{\gamma }}$

(4) $\frac{{P}_{2}{\left(\frac{{V}_{0}}{2}\right)}^{\gamma }}{{\left(\frac{{V}_{0}}{2}+Ax\right)}^{\gamma }}$

Concept Questions :-

Types of processes
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Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is

(1) 30 K

(2) 18 K

(3) 50 K

(4) 42 K

Concept Questions :-

Molar Specific heat
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A system goes from A to B via two processes I and II as shown in figure. If ΔUI and ΔUII are the changes in internal energies in the processes I and II respectively, then

(1) ΔUII > ΔUI

(2) ΔUII < ΔUI

(3) ΔUI = ΔUII

(4) Relation between ΔUI and ΔUII can not be determined

Concept Questions :-

Basic terms
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A thermodynamic system is taken through the cycle PQRSP process. The net work done by the system is -

(1) 20 J

(2) – 20 J

(3) 400 J

(4) – 374 J

Concept Questions :-

Cyclic process
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An ideal gas is taken around ABCA as shown in the above P-V diagram. The work done during a cycle is

(1) 2PV

(2) PV

(3) 1/2PV

(4) Zero

Concept Questions :-

Cyclic process