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For hydrogen gas C(P)-C(V)=alpha and for...

For hydrogen gas `C_(P)-C_(V)=alpha` and for Oxygen gas `C_(P)-C_(V)=b`, where `C_(P)` and `C_(V)` are molar specific heats. Then the relation between 'a' and 'b' is

A

`a = 16 b`

B

`16 b = a`

C

`a = 4b`

D

`a = b`

Text Solution

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The correct Answer is:
To solve the problem, we need to understand the relationship between the molar specific heats at constant pressure (C_P) and constant volume (C_V) for gases. The difference between these two specific heats is given by the equation: \[ C_P - C_V = R \] where R is the universal gas constant. ### Step-by-Step Solution: 1. **Identify the given information:** - For hydrogen gas, we have: \[ C_P - C_V = \alpha \] - For oxygen gas, we have: \[ C_P - C_V = b \] 2. **Use the relationship for ideal gases:** - According to the ideal gas law, for any ideal gas, the difference between the molar specific heats at constant pressure and constant volume is equal to the universal gas constant R: \[ C_P - C_V = R \] 3. **Apply this relationship to both gases:** - For hydrogen gas: \[ \alpha = R \] - For oxygen gas: \[ b = R \] 4. **Establish the relationship between α and b:** - Since both α and b are equal to R, we can conclude: \[ \alpha = b \] 5. **Final conclusion:** - Therefore, the relation between 'a' and 'b' is: \[ \alpha = b \]
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