Heat And Thermodynamics Ques 2
- An ideal gas occupies a volume of $2 \mathrm{~m}^3$ at a pressure of $3 \times 10^6 \mathrm{~Pa}$. The energy of the gas is
$\quad$ (2019 Main, 12 Jan I)
(a) $6 \times 10^4 \mathrm{~J}$
(b) $10^8 \mathrm{~J}$
(c) $9 \times 10^6 \mathrm{~J}$
(d) $3 \times 10^2 \mathrm{~J}$
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Answer:
Correct Answer: 2.( c )
Solution:
Formula:
Total Translational K.E. Of Gas
- Key Idea Internal energy of ’ $n$ ’ moles of a gas with degree of freedom $f$ ( $=3$ for an ideal gas), at temperature $T$ is
$ E=\frac{f}{2} \cdot n R T=\frac{3}{2} n R T $
For an ideal gas, internal energy, $E=\frac{3}{2} n R T$
$ =\frac{3}{2} p \cdot V \quad(\because \text { from } p V=n R T) $
Substituting the given values, we get
$ =\frac{3}{2} \times 3 \times 10^6 \times 2=9 \times 10^6 \mathrm{~J} $
BETA
