When 300 J of heat is given to an ideal gas with its temperature raises from to keeping its volume constant. The mass of the gas is (approximately) g. () [2026]

Question

When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]

Smart Achievers · Accepted Answer

(481)

$For a constant volume process, the heat supplied (Q) is given by the formula:$

$20 ° C$

$Where:$

1. $n$ = number of moles of the gas.
2. $C_{v}$ = molar specific heat capacity at constant volume.
3. $Δ T$ = change in temperature $= 50 ° C - 20 ° C = 30 ° C = 30 K$

We are given the molar specific heat at constant pressure, $C_{p} = \frac{7}{2} R .$ Using Mayer's relation $(C_{p} - C_{v} = R)$ :

$C_{v} = C_{p} - R$

$\Rightarrow C_{v} = \frac{7}{2} R - R = \frac{5}{2} R$

Using the formula of heat,

$300 = n \times (\frac{5}{2} \times 8.314) \times 30$

$n = \frac{300 \times 2}{5 \times 8.314 \times 30} \approx 0.481 moles$

So, the amount of the gas is 0.481 moles. As the molar mass of the gas is not given in the question, we can't determine the mass of the gas directly.

Solution

Q.
When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]

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Solution

Q. When 300 J of heat is given to an ideal gas with Cp=72R its temperature raises from 20°C to 50°C keeping its volume constant. The mass of the gas is (approximately) _______ g. (R=8.314 J/mol.K) [2026]

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Q.
When 300 J of heat is given to an ideal gas with $C_{p} = \frac{7}{2} R$ its temperature raises from $20 ° C$ to $50 ° C$ keeping its volume constant. The mass of the gas is (approximately) _______ g. ( $R = 8.314 J/mol.K$ ) [2026]