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The molar specific heat at a constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume is
- a)8/7
- b)5/7
- c)9/7
- d)7/5
Correct answer is option 'D'. Can you explain this answer?
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The molar specific heat at a constant pressure of an ideal gas is (7/...
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Mayer’s Equation for an ideal gas:
Cp – Cv = R
The ratio of Specific heat is known as an adiabatic index.
γ = Cp/Cv
Calculation:
Cp = 7/2R
Cv = Cp − R = 7/2R − R = 5/2R
γ = Cp/Cv = 7/5 = 1.4
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The molar specific heat at a constant pressure of an ideal gas is (7/...
The specific heat (C) of a substance is the amount of heat energy required to raise the temperature of a given mass of the substance by 1 degree Celsius. It is defined as the ratio of the heat energy transferred (Q) to the change in temperature (ΔT) and the mass (m) of the substance:
C = Q / (m * ΔT)
The molar specific heat (Cm) is the specific heat per mole of the substance. In the case of an ideal gas, the molar specific heat at constant pressure (Cp) and constant volume (Cv) are related by the equation:
Cp - Cv = R
where R is the gas constant.
Given that Cp = (7/2)R, we can substitute this value into the equation and solve for Cv:
(7/2)R - Cv = R
Simplifying the equation, we find:
Cv = (5/2)R
The ratio of specific heat at constant pressure to that at constant volume is given by:
Cp / Cv = (7/2)R / (5/2)R = 7/5
Therefore, the correct answer is option 'D' (7/5).
In summary:
- The molar specific heat at constant pressure (Cp) of an ideal gas is (7/2)R.
- The molar specific heat at constant volume (Cv) can be found by subtracting the gas constant (R) from Cp: Cv = (7/2)R - R = (5/2)R.
- The ratio of Cp to Cv is Cp / Cv = (7/2)R / (5/2)R = 7/5.
C = Q / (m * ΔT)
The molar specific heat (Cm) is the specific heat per mole of the substance. In the case of an ideal gas, the molar specific heat at constant pressure (Cp) and constant volume (Cv) are related by the equation:
Cp - Cv = R
where R is the gas constant.
Given that Cp = (7/2)R, we can substitute this value into the equation and solve for Cv:
(7/2)R - Cv = R
Simplifying the equation, we find:
Cv = (5/2)R
The ratio of specific heat at constant pressure to that at constant volume is given by:
Cp / Cv = (7/2)R / (5/2)R = 7/5
Therefore, the correct answer is option 'D' (7/5).
In summary:
- The molar specific heat at constant pressure (Cp) of an ideal gas is (7/2)R.
- The molar specific heat at constant volume (Cv) can be found by subtracting the gas constant (R) from Cp: Cv = (7/2)R - R = (5/2)R.
- The ratio of Cp to Cv is Cp / Cv = (7/2)R / (5/2)R = 7/5.
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The molar specific heat at a constant pressure of an ideal gas is (7/2) R. The ratio of specific heat at constant pressure to that at constant volume isa)8/7b)5/7c)9/7d)7/5Correct answer is option 'D'. Can you explain this answer?
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