Two cylinders $$A$$ and $$B$$ fitted with pistons contain equal amounts of an ideal diatomic gas at $$300\,K.$$ The piston of $$A$$ is free to move while that of $$B$$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $$A$$ is $$30\,K,$$ then the rise in temperature of the gas in $$B$$ is
A.
$$30\,K$$
B.
$$18\,K$$
C.
$$50\,K$$
D.
$$42\,K$$
Answer :
$$42\,K$$
Solution :
$$\eqalign{
& Q = n{C_P} \times 30 = n \times \frac{{7R}}{2} \times 30 \cr
& {\text{and }}Q = n \times \frac{{5R}}{2} \times \Delta T \cr
& \therefore n \times \frac{{7R}}{2} \times 30 = n \times \frac{{5R}}{2} \times \Delta T\,\,{\text{or}}\,\,\Delta T = 42\,K. \cr} $$
Releted MCQ Question on Heat and Thermodynamics >> Thermodynamics
Releted Question 1
An ideal monatomic gas is taken round the cycle $$ABCDA$$ as shown in the $$P - V$$ diagram (see Fig.). The work done during the cycle is
If one mole of a monatomic gas $$\left( {\gamma = \frac{5}{3}} \right)$$ is mixed with one mole of a diatomic gas $$\left( {\gamma = \frac{7}{5}} \right)$$ the value of $$\gamma $$ for mixture is
A closed compartment containing gas is moving with some acceleration in horizontal direction. Neglect effect of gravity. Then the pressure in the compartment is
A gas mixture consists of 2 moles of oxygen and 4 moles of argon at temperature $$T.$$ Neglecting all vibrational modes, the total internal energy of the system is