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1

AIEEE 2005

MCQ (Single Correct Answer)
A gaseous mixture consists of $$16$$ $$g$$ of helium and $$16$$ $$g$$ of oxygen. The ratio $${{Cp} \over {{C_v}}}$$ of the mixture is
A
$$1.62$$
B
$$1.59$$
C
$$1.54$$
D
$$1.4$$

Explanation

$${{{n_1} + {n_2}} \over {r - 1}} = {{{n_1}} \over {{r_1} - 1}} + {{{n_2}} \over {{r_2} - 1}}$$
$${{{{16} \over 4} + {{16} \over {32}}} \over {r - 1}} = {{16/4} \over {{5 \over 3} - 1}} + {{16/32} \over {1.4 - 1}}$$
$$\therefore$$ $$\gamma = 1.62$$
2

AIEEE 2004

MCQ (Single Correct Answer)
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $$K$$ and $$2K$$ and thickness $$x$$ and $$4x,$$ respectively, are $${T_2}$$ and $${T_1}\left( {{T_2} > {T_1}} \right).$$ The rate of heat transfer through the slab, in a steady state is $$\left( {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right)f,$$ with $$f$$ equal to
A
$${2 \over 3}$$
B
$${1 \over 2}$$
C
$$1$$
D
$${1 \over 3}$$

Explanation

The thermal resistance
$${x \over {KA}} + {{4x} \over {2KA}} = {{3x} \over {KA}}$$
$$\therefore$$ $${{dQ} \over {dt}} = {{\Delta T} \over {{{3x} \over {KA}}}} = {{\left( {{T_2} - {T_1}} \right)KA} \over {3x}}$$
$$ = {1 \over 3}\left\{ {{{A\left( {{T_2} - {T_1}} \right)K} \over x}} \right\}$$
$$\therefore$$ $$f = {1 \over 3}$$
3

AIEEE 2004

MCQ (Single Correct Answer)
Which of the following statements is correct for any thermodynamic system ?
A
The change in entropy can never be zero
B
Internal energy and entropy and state functions
C
The internal energy changes in all processes
D
The work done in an adiabatic process is always zero,

Explanation

Internal energy and entropy are state function, they do not depend upon path taken.
4

AIEEE 2004

MCQ (Single Correct Answer)
Two thermally insulated vessels $$1$$ and $$2$$ are filled with air at temperatures $$\left( {{T_1},{T_2}} \right),$$ volume $$\left( {{V_1},{V_2}} \right)$$ and pressure $$\left( {{P_1},{P_2}} \right)$$ respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
A
$${T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}} \right)$$
B
$$\left( {{T_1} + {T_2}} \right)/2$$
C
$${{T_1} + {T_2}}$$
D
$${T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)/\left( {{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \right)$$

Explanation

Here $$Q=0$$ and $$W=0.$$ Therefore from first law of thermodynamics $$\Delta U = Q + W = 0$$
$$\therefore$$ Internal energy of the system with partition $$=$$ Internal energy of the system without partition.
$${n_1}{C_v}\,{T_1} + {n_2}\,{C_v}{T_2} = \left( {{n_1} + {n_2}} \right){C_v}\,T$$
$$\therefore$$ $$T = {{{n_1}{T_1} + {n_2}T{}_2} \over {{n_1} + {n_2}}}$$
But $${n_1} = {{{P_1}{V_1}} \over {R{T_1}}}$$ and $${n_2} = {{{P_2}{V_2}} \over {R{T_2}}}$$
$$\therefore$$ $$T = {{{{{P_1}{V_1}} \over {R{T_1}}} \times {T_1} + {{{P_2}{V_2}} \over {R{T_2}}} \times {T_2}} \over {{{{P_1}{V_1}} \over {R{T_1}}} + {{{P_2}{V_2}} \over {R{T_2}}}}}$$
$$ = {{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}$$

Questions Asked from Heat and Thermodynamics

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