Question 569: Thermodynamics & KTG

Question

An engine takes in 5 moles of air at 20
o
C and
1 atm, and compresses it adiabatically to
1/10
th
of the original volume. Assuming air to
be a diatomic ideal gas made up of rigid
molecules, the change in its internal energy
during this process comes out to be X kJ. The
value of X to the nearest integer is________.

Accepted Answer

For diatomic ideal gas :
f = 5
$$\gamma $$ = $${7 \over 5}$$
T
i
= T = 273 + 20 = 293 K
V
i
= V
V
f
= $${V \over {10}}$$
For adiabatic process TV
$$\gamma $$ - 1
= constant
$${T_1}V_1^{\gamma  - 1} = {T_2}V_2^{\gamma  - 1}$$
$$ \Rightarrow $$ $$\left( {293} ight){V^{{7 \over 5} - 1}} = {T_2}{\left( {{V \over {10}}} ight)^{{7 \over 5} - 1}}$$
$$ \Rightarrow $$ $${T_2} = 293 	imes {\left( {10} ight)^{{2 \over 5}}}$$
$$\Delta $$U = $${{nfR\left( {{T_2} - {T_1}} ight)} \over 2}$$
= $${{5 	imes 5 	imes {{25} \over 3} 	imes \left( {{{293.10}^{{2 \over 5}}} - 293} ight)} \over 2}$$
= $${{625 	imes 293 	imes \left( {{{10}^{{2 \over 5}}} - 1} ight)} \over 6}$$
= 46.14 $$ 	imes $$ 10
3
J
$$ \simeq $$ 46 kJ

Thermodynamics & KTG

Integer / Numeric Answer Type