An ideal gas goes from state \(A\) to state \(B\) via three different processes, as indicated in the \(P\text-V\) diagram. If \(Q_1,Q_2,Q_3\)${\mathrm{}}_{}$ indicates the heat absorbed by the gas along the three processes and \(\Delta U_1, \Delta U_2, \Delta U_3\) indicates the change in internal energy along the three processes respectively, then:

           

1.	\({Q}_1>{Q}_2>{Q}_3 \) and \(\Delta {U}_1=\Delta {U}_2=\Delta {U}_3\)
2.	\({Q}_3>{Q}_2>{Q}_1\)  and \(\Delta {U}_1=\Delta {U}_2=\Delta {U}_3\)
3.	\({Q}_1={Q}_2={Q}_3\) and \(\Delta {U}_1>\Delta {U}_2>\Delta {U}_3\)
4.	\({Q}_3>{Q}_2>{Q}_1\) and \(\Delta {U}_1>\Delta {U}_2>\Delta {U}_3\)

A mass of diatomic gas ($\gamma$=1.4) at a pressure of 2 atm is compressed adiabatically so that its temperature rise from $27°\mathrm{C}$ to $927°\mathrm{C}.$ The pressure of the gas is final state is-

(1) 28 atm                                           

(2) 68.7 atm

(3) 256 atm                                           

(4) 8 atm

If $∆U and ∆W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process,which of the following is true?

(1) $∆U=-∆W,$ in a adiabatic process

(2) $∆U=∆W,$ in a isothermal process

(3) $∆U=∆W,$ in adiabatic process

(4) $∆U=-∆W,$in a isothermal process 

A monoatomic gas at pressure ${\mathrm{p}}_1$ and ${\mathrm{V}}_1$ is compressed adiabatically to $\frac{1}{8}\mathrm{th}$ its original volume. What is the final pressure of the gas ?

1, $64 {\mathrm{p}}_1$                                   

2. ${\mathrm{p}}_1$

3. $16 {\mathrm{p}}_1$                                   

4. $32 {\mathrm{p}}_1$

The internal energy change in a system that has absorbed 2 kcal of heat and done 500 J of work is 

1. 8900 J                                     

2. 6400 J

3. 5400 J                                     

4. 7900 J

In thermodynamic processes, which of the following statements is not true?

If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then

1. W=0                                 

2. Q=W=0

3. E=0                                   

4. Q=0

The specific heat at constant pressure and at constant volume for an ideal gas are $C_p$ and $C_v$ and its adiabatic and isothermal elasticities are $E_{\varnothing }$ and$E_{\theta }$  respectively. The  ratio of $E_{\varnothing }$ to $E_{\theta }$ is

1. $C_v/C_p$

2. $C_p/C_v$

3. $C_p{C}_v$

4. $1/C_p{C}_v$

If the volume of the given mass of a gas is increased four times and the temperature is raised from 27°C to 127°C. The isothermal elasticity will become

1. 4 times                               

2. 1/4 times

3. 3 times                               

4. 1/3 times

A system performs work ΔW when an amount of heat is ΔQ added to the system, the corresponding change in the internal energy is ΔU. A unique function of the initial and final states (irrespective of the mode of change) is -

(1) ΔQ

(2) ΔW

(3) ΔU and ΔQ

(4) ΔU