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The molar specific heat at 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 [2006]
Correct answer is option 'D'. Can you explain this answer?
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The molar specific heat at constant pressure of an ideal gas is (7/2) ...
The molar specific heat at constant pressure of an ideal gas is given as (7/2) R, where R is the gas constant. We need to find the ratio of specific heat at constant pressure to that at constant volume.
To understand this, let's start by defining the specific heat at constant pressure (Cp) and specific heat at constant volume (Cv).
Specific heat at constant pressure (Cp):
Cp is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant pressure. It is given by the equation:
Cp = q / (n * ΔT)
where q is the heat absorbed or released, n is the number of moles of the substance, and ΔT is the change in temperature.
Specific heat at constant volume (Cv):
Cv is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant volume. It is given by the equation:
Cv = q / (n * ΔT)
where q is the heat absorbed or released, n is the number of moles of the substance, and ΔT is the change in temperature.
The ratio of Cp to Cv can be calculated by dividing the equation for Cp by the equation for Cv:
(Cp/Cv) = (q / (n * ΔT)) / (q / (n * ΔT))
(Cp/Cv) = (q / (n * ΔT)) * ((n * ΔT) / q)
(Cp/Cv) = (n * ΔT) / (n * ΔT)
(Cp/Cv) = 1
From the equation, we can see that the ratio of Cp to Cv for an ideal gas is always equal to 1. However, in the given question, it is stated that Cp = (7/2) R. Therefore, we can write:
(7/2) R / Cv = 1
Cv = (7/2) R / (1)
Cv = (7/2) R
So, the ratio of specific heat at constant pressure to that at constant volume is 7/2, which can be written as 7/5 in simplified form. Therefore, the correct answer is option 'D' (7/5).
To understand this, let's start by defining the specific heat at constant pressure (Cp) and specific heat at constant volume (Cv).
Specific heat at constant pressure (Cp):
Cp is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant pressure. It is given by the equation:
Cp = q / (n * ΔT)
where q is the heat absorbed or released, n is the number of moles of the substance, and ΔT is the change in temperature.
Specific heat at constant volume (Cv):
Cv is the amount of heat required to raise the temperature of a substance by 1 degree Celsius at constant volume. It is given by the equation:
Cv = q / (n * ΔT)
where q is the heat absorbed or released, n is the number of moles of the substance, and ΔT is the change in temperature.
The ratio of Cp to Cv can be calculated by dividing the equation for Cp by the equation for Cv:
(Cp/Cv) = (q / (n * ΔT)) / (q / (n * ΔT))
(Cp/Cv) = (q / (n * ΔT)) * ((n * ΔT) / q)
(Cp/Cv) = (n * ΔT) / (n * ΔT)
(Cp/Cv) = 1
From the equation, we can see that the ratio of Cp to Cv for an ideal gas is always equal to 1. However, in the given question, it is stated that Cp = (7/2) R. Therefore, we can write:
(7/2) R / Cv = 1
Cv = (7/2) R / (1)
Cv = (7/2) R
So, the ratio of specific heat at constant pressure to that at constant volume is 7/2, which can be written as 7/5 in simplified form. Therefore, the correct answer is option 'D' (7/5).
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Community Answer
The molar specific heat at constant pressure of an ideal gas is (7/2) ...
Cp = 7R/2 so Cv = 5R/2 (Cp-Cv = R)
So Cp/Cv = 7/5
So Cp/Cv = 7/5
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The molar specific heat at 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)7/5 [2006]Correct answer is option 'D'. Can you explain this answer?
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