Two moles of ideal helium gas are in a rubber balloon at $${30^ \circ }C.$$ The balloon is fully expandable and can be assumed to require no energy in its expansion. The temperature of the gas in the balloon is slowly changed to $${35^ \circ }C.$$ The amount of heat required in raising the temperature is nearly (take $$R = 8.31\,J/mol.K$$ )
A.
$$62\,J$$
B.
$$104\,J$$
C.
$$124\,J$$
D.
$$208\,J$$
Answer :
$$208\,J$$
Solution :
The heat is supplied at constant pressure. Therefore,
$$\eqalign{
& Q = n{C_p}\Delta t \cr
& = 2\left[ {\frac{5}{2}R} \right] \times \Delta t \cr
& = 2 \times \frac{5}{2} \times 8.31 \times 5 \cr
& = 208\,J\,\left( {\because {C_p} = \frac{5}{2}R\,{\text{for mono - atomic gas}}} \right) \cr} $$
Releted MCQ Question on Heat and Thermodynamics >> Kinetic Theory of Gases
The average translational kinetic energy of $${O_2}$$ (relative molar mass 32) molecules at a particular temperature is $$0.048\,eV.$$ The translational kinetic energy of $${N_2}$$ (relative molar mass 28) molecules in $$eV$$ at the same temperature is
A vessel contains 1 mole of $${O_2}$$ gas (relative molar mass 32) at a temperature $$T.$$ The pressure of the gas is $$P.$$ An identical vessel containing one mole of $$He$$ gas (relative molar mass 4) at a temperature $$2\,T$$ has a pressure of