0.040 g of He is kept in a closed container initially at 100.0°C. The container is now heated. Neglecting the expansion of the container, calculate the temperature at which the internal energy is increased by 12 J.

Given

Mass of helium =0.040g

Molar mass of helium=4g/mol

Number of moles n=

Number of moles for helium n=

Temperature T₁=100

T(K)=T ()+273.15

T=T(K)=100+273.15=373.15K

Internal energy U in kinetic theory is given as

Where C_v= molar specific heat capacity

N= number of moles

T=temperature of gas

Also, internal energy depends only the temperature of the gas.

Helium is a monoatomic gas and for monoatomic gas

So, C_v for helium is Jmol^-1K^-1

Increase in internal energy is given in question as 12J. That means

U₂-U₁= nC_v(T₂-T₁)

Since the gas has not been changed, just expanded no change in molar specific heat capacity and number of moles of gas.

Putting the value of change in internal energy and T_1,

12=0.0112.45(T₂-373.15)

The temperature at which the internal energy is increased by 12J is 469.53J =196.38.