Two cylinders contain the same amount of an ideal monoatomic gas. The same amount of heat is given to two cylinders. If the temperature rise in cylinder A is T₀, then the temperature rise in cylinder B will be:

1. $\frac{4}{3}{\mathrm{T}}_0$

2. $2{\mathrm{T}}_0$

3. $\frac{{\mathrm{T}}_0}{2}$

4. $\frac{5}{3}{\mathrm{T}}_0$

The pressure and volume of a gas are changed as shown in the P-V diagram. The temperature of the gas will:

The incorrect relation is:
(where symbols have their usual meanings)

1. ${\mathrm{C}}_{\mathrm{P}}=\frac{\mathrm{\gamma R}}{\mathrm{\gamma }-1}$

2. ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{R}$

3. $∆\mathrm{U}=\frac{{\mathrm{P}}_{\mathrm{f}}{\mathrm{V}}_{\mathrm{f}}-{\mathrm{P}}_{\mathrm{i}}{\mathrm{V}}_{\mathrm{i}}}{1-\mathrm{\gamma }}$

4. ${\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{\gamma }-1}$

The figure shows the (P-V) diagram of an ideal gas undergoing a change of state from A to B. Four different paths I, II, III and IV, as shown in the figure, may lead to the same change of state.
               

Which of the following options contains only correct statements?

Consider a cycle followed by an engine (figure). 

1 to 2 is isothermal,

2 to 3 is adiabatic,

3 to 1 is adiabatic.

Such a process does not exist, because:

Choose the correct alternatives:
1. (a, b)
2. (a, c)
3. (b, c)
4. (c, d)

Two cylinders, A and B, of equal capacity are connected to each other via a stopcock. A contains gas at a standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. If the stopcock is suddenly opened, then the change in internal energy of the gas is:

When a bicycle tyre suddenly bursts, the air inside the tyre expands. This process is:
1. isothermal
2. adiabatic
3. isobaric
4. isochoric

Find out the total heat given to diatomic gas in the process A$\to$B$\to$C : (B$\to$C is isothermal)
                 

1. ${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$

2. $\frac{1}{2}$${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0\ln 2$

3. $\frac{5}{2}$${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$

4. 3${\mathrm{P}}_0{\mathrm{V}}_0+2{\mathrm{P}}_0{\mathrm{V}}_0$ $\ln 2$

The efficiency of a Carnot engine is 40% when it receives energy at 500 K. At what temperature it should receive energy  to increase its efficiency by 25% ?

At a pressure of \(2\) atmospheres, a mass of diatomic gas \((\gamma = 1.4)\), is compressed adiabatically, causing its temperature to rise from \(27^{\circ}\mathrm{C}\) to \(927^{\circ}\mathrm{C}\). The pressure of the gas in the final state is:
1. 8 atm
2. 28 atm
3. 68.7 atm
4. 256 atm