One kg of a diatomic gas is at a pressure of 8 × 104 N/m2. The density of the gas is 4 kg/m3. What is the energy of the gas due to its thermal motion?

Question

One kg of a diatomic gas is at a pressure of 8 × 104 N/m2. The density of the gas is 4 kg/m3. What is the energy of the gas due to its thermal motion? (A) 3 × 104 J (B) 6 × 104 J (C) 5 × 104 J (D) 7 × 104 J

Tardigrade Admin · Accepted Answer

Thermal energy corresponds to internal energy Mass = 1 kg density = 8 kg/m3 ⇒ Volume=(mass/density)=(1/8)m3 Pressure = 8 Ã 104 N/m2 ∴ Internal Energy =(5/2)P Ã V = 5 Ã 104 J

Q. One $k g$ of a diatomic gas is at a pressure of $8 \times 1 0^{4} N / m^{2}$ . The density of the gas is $4 k g / m^{3}$ . What is the energy of the gas due to its thermal motion?

$3 \times 1 0^{4} J$

$6 \times 1 0^{4} J$

$5 \times 1 0^{4} J$

$7 \times 1 0^{4} J$

Thermal energy corresponds to internal energy
Mass $= 1 k g$
density $= 8 k g / m^{3}$
$\Rightarrow V o l u m e = \frac{ma ss}{d e n s i t y} = \frac{1}{8} m^{3}$
Pressure $= 8 \times 1 0^{4} N / m^{2}$
$∴$ Internal Energy $= \frac{5}{2} P \times V = 5 \times 1 0^{4} J$

Q. One kg of a diatomic gas is at a pressure of 8×104N/m2. The density of the gas is 4kg/m3. What is the energy of the gas due to its thermal motion?

3×104J

6×104J

5×104J

7×104J