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The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal/g-°C and 3.4 cal/g-°C respectively. The molecular weight of hydrogen is 2 g/mol and the gas constant R = 8.3 × 107 erg/mol-°C. Calculate the value of J.

The specific heat capacities of hydrogen at constant volume and at constant pressure are 2.4 cal/g-°C and 3.4 cal/g-°C respectively. The molecular weight of hydrogen is 2 g/mol and the gas constant R = 8.3 × 107 erg/mol-°C. Calculate the value of J.

Grade:upto college level

3 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
Sol. C base VH base 2 = 2.4 Cal/g°C, C base PH^2 = 3.4 Cal/g°C M = 2 g/ Mol, R = 8.3 × 10^7 erg/mol-°C We know, C base P – C base V = 1 Cal/g°C So, difference of molar specific heats = C base P × M – CV × M = 1 × 2 = 2 Cal/g°C Now, 2 × J = R ⇒ 2 × J = 8.3 × 107 erg/mol-°C ⇒ J = 4.15 × 107 erg/cal.
Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Sol. γ = 1.4, w or piston = 50 kg., A of piston = 100 cm2 Po = 100 kpa, g = 10 m/s2, x = 20 cm. dw = pdv = (mg/A + Po)Adx = (50 * 10/100 * 10^-4 + 10^5)100 * 10^-4 * 20 * 10^-2 = 1.5 * 10^5 * 20 * 10^-4 = 300 J. nRdt = 300 ⇒ dT = 300/nR dQ = nCpdT = nCp * 300/nR = nγR300/(γ - 1)nR = 300 * 1.4/0.4 = 1050 J.
Navjyot Kalra
askIITians Faculty 654 Points
7 years ago
Sol C base VH base 2 = 2.4 Cal/g°C, C base PH^2 = 3.4 Cal/g°C M = 2 g/ Mol, R = 8.3 × 10^7 erg/mol-°C We know, C base P – C base V = 1 Cal/g°C So, difference of molar specific heats = C base P × M – CV × M = 1 × 2 = 2 Cal/g°C Now, 2 × J = R ⇒ 2 × J = 8.3 × 107 erg/mol-°C ⇒ J = 4.15 × 107 erg/cal.

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