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

A container of volume 1m³ is divided into two equal compartments by a partition. One of these compartments contains an ideal gas at 300 K. The other compartment is vaccum. The whole system is thermally isolated from its surroundings. The partition is removed and the gas expands to occupy the whole volume of the container. Its temperature now would be -

(1) 300 K

(2) 239 K

(3) 200 K

(4) 100 K

110 J of heat is added to a gaseous system, whose internal energy change is 40 J, then the amount of external work done is 

(1) 150 J

(2) 70 J

(3) 110 J

(4) 40 J