Heat Capacity

The internal energy $\left(U\right)$, pressure $\left(P\right)$ and volume $\left(V\right)$ of an ideal gas are related as $U=3PV+4$. The gas is:

1. Polyatomic only

2. Monoatomic only

3. Either monoatomic or diatomic

4. Diatomic only

$\frac{1}{2}$ mole of helium gas is contained in a container at S.T.P. The heat energy needed to double the pressure of the gas, keeping the volume constant (specific heat of the gas = $3Jg{m}^{-1}{K}^{-1}$) is

1. 409.5 J

2. 3276 J

3. 1638 J

4. 819 J

The specific heat of an ideal gas is

1. Proportional to T

2. 

3. 

4. Independent of T

Gas at a pressure $P_0$, in contained is a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

1. $1.47$
2. $1.42$
3. $1.45$
4. $1.50$

At constant volume the specific heat of a gas is $\frac{3R}{2}$, then the value of $\gamma$ will be

A system receives heat continuously at the rate of 10W. The temperature of the system becomes constant at ${70}^{\circ }C$ when the temperature of the surroundings is ${30}^{\circ }C$. After the heater is switched off, the system cools from ${50}^{\circ }C$ to ${49.9}^{\circ }C$ in 1 min. The heat capacity of the system is

1. 1000 J/°C

2. 1500 J/°C

3. 3000 J/°C

4. None of these

A drilling machine of 10kW power is used to drill a bore in a small aluminium block of mass 8kg. If 50% of power is used up in heating the machine itself of lost to the surroundings then how much is the rise in temperature of the block in 2.5 min(given: specific heat of aluminium=0.91 $J/g^{\circ }C$)?

1. 103°C

2. 130°C

3. 105°C

4. 30°C