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AIEEE 2003

MCQ (Single Correct Answer)
A carnot engine takes $$3 \times {10^6}$$ cal. of heat from a reservoir at $${627^ \circ }C,$$ and gives it to a sink at $${27^ \circ }C$$. The work done by the engine is
A
$$4.2 \times {10^6}J$$
B
$$8.4 \times {10^6}J$$
C
$$16.8 \times {10^6}J$$
D
zero

Explanation

$$\eta = 1 - {{{T_2}} \over {{T_1}}}$$

$$ = 1 - {{\left( {273 + 27} \right)} \over {\left( {273 + 627} \right)}}$$

$$ = 1 - {{300} \over {900}}$$

$$ = 1 - {1 \over 3} = {2 \over 3}$$

But $$\eta = {W \over Q}$$

$$\therefore$$ $${W \over Q} = {2 \over 3} \Rightarrow W$$

$$ = {2 \over 3} \times Q$$

$$ = {2 \over 3} \times 3 \times {10^6}$$

$$ = 2 \times {10^6}cal$$

$$ = 2 \times {10^6} \times 4.2\,J$$

$$ = 8.4 \times {10^6}J$$
2

AIEEE 2003

MCQ (Single Correct Answer)
Which of the following parameters does not characterize the thermodynamic state of mattter?
A
Temperature
B
Pressure
C
Work
D
Volume

Explanation

Work is a path function. The remaining three parameters are state function.
3

AIEEE 2003

MCQ (Single Correct Answer)
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio $${C_p}/{C_V}$$ for the gas is
A
$${4 \over 3}$$
B
$$2$$
C
$${5 \over 3}$$
D
$${3 \over 2}$$

Explanation

$$P \propto {T^3} \Rightarrow P{T^{ - 3}} = $$ constant ....$$(i)$$
But for an adiabatic process, the pressure temperature relationship is given by
$${P^{1 - \gamma }}\,\,{T^\gamma } = $$ constant $$ \Rightarrow P{T^{{\gamma \over {1 - \gamma }}}} = $$ constant. ....$$(ii)$$
From $$(i)$$ and $$(ii)$$ $${\gamma \over {1 - \gamma }} = - 3 \Rightarrow \gamma = - 3 + 3\gamma \Rightarrow \gamma = {3 \over 2}$$
4

AIEEE 2003

MCQ (Single Correct Answer)
''Heat cannot by itself flow from a body at lower temperature to a body at higher temperature'' is a statement or consequence of
A
second law of thermodynamics
B
conservation of momentum
C
conservation of mass
D
first law of thermodynamics

Explanation

This is a statement of second law of thermodynamics

Questions Asked from Heat and Thermodynamics

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