Q: A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 16 81 . Then the ratio of

In adiabatic process aligned & PV ^ = constant \\ & P _1 ~V _1^ = P _2 ~V _2^ \\ & P _1 P _2 = ( V _2 ~V _1 )^ 81 16 = ( 27 8 )^ \\ & ( 9 4 )^2= ( 9 3 4 2 )^ ( 9 4 )^ 2- = ( 3 2 )^ \\ & ( 9 4 )^ 2- = ( 9 4 )^ / 2 2- = 2 \\ & 2= 3 2 = 4 3 aligned

Question 1

In the given cycle A B C D A, the heat required for an ideal monoatomic gas will be

Accepted Answer

In the given cycle, heat is supplied in process D to A at constant volume and in process A to B at constant pressure. Heat supplied, Q=n C_V( T)_ D A +n C_p( T)_ A B For an ideal monoatomic gas, aligned C_V & = 3 2 R and C_p= 5 2 R \ Q & = 3 2 n R T+ 5 2 n R T [ n R T=p V] \ & = 3 2 (p_0 V_0 )+5 (p_0 V_0 ) \ & = 13 2 p_0 V_0 aligned

Question 2

A gas can be taken from A to B via two different processes A C B and A D B. When path A C B is used 60 J of heat flows into the system and 30J of work is done by the system. If path ADB is used work d

Accepted Answer

U remains same for both paths ACB and ADB Q_ A C B = W_ A C B + U_ A C B 60 ~J =30 ~J + U _ ACB U _ ACB =30 ~J As change in internal energy depends only on initial and final point U _ ADB = U _ ACB =30 ~J Q _ ADB = U _ ADB + W _ ADB =10 ~J +30 ~J =40 ~J

Question 3

A source supplies heat to a system at the rate of 1000 W . If the system performs work at a rate of 200 W . The rate at which internal energy of the system increases

Accepted Answer

Given, Rate of heat supplied, dQ dt =1000 ~W Rate of work performed, dw dt =200 ~W Using first law of thermodynamics d Q=d U+d w $ dU dt = dQ dt - dw dt dU dt =1000-200=800$

Question 4

On celcius scale the temperature of body increases by 40^ C . The increase in temperature on Fahrenheit scale is:

Accepted Answer

Since F-32 9 = C 5 C = 5 9 ~F 40= 5 9 ~F ~F =72^ F

Question 5

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 16 81 . Then the ratio of

Accepted Answer

In adiabatic process aligned & PV ^ = constant \ & P _1 ~V _1^ = P _2 ~V _2^ \ & P _1 P _2 = ( V _2 ~V _1 )^ 81 16 = ( 27 8 )^ \ & ( 9 4 )^2= ( 9 3 4 2 )^ ( 9 4 )^ 2- = ( 3 2 )^ \ & ( 9 4 )^ 2- = ( 9 4 )^ / 2 2- = 2 \ & 2= 3 2 = 4 3 aligned

Question 6

A thermodynamic system is taken through cyclic process. The total work done in the process is :

Accepted Answer

Work done = Area under the curve W = 1 2 (4-2) (400-100)= 1 2 (2) 300 W =300 ~J

Question 7

An ideal gas at atmospheric pressure is adiabatically compressed so that its density becomes 32 times of its initial value. If the final pressure of gas is 128 atmospheres, the value of ' ' of the gas

Accepted Answer

Volume v= m d and using PV ^ = constant array l P ^ P = V V ^ = ( d ^ d )^ \ or 128=(32)^ \ = 7 5 =1.4 array

Question 8

The compressibility of water is 4 10^ -5 per unit atmospheric pressure. The decrease in volume of 100 ~cm ^ 3 of water under a pressure of 100 atmosphere will be

Accepted Answer

Compressibility = 1 ~B = V / V P . Here, P =100 ~atm Compressibility =4 10^ -5 and V =100 ~cm ^ 3 Hence, V =0.4 ~cm ^ 3

Thermodynamics — Previous Year Questions & Solutions