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For 1 mole of ideal gas which of the fol...

For 1 mole of ideal gas which of the following statements must be true
a) U & H depend only on temperature
b) Compressibility factor (Z) can not be 1.
c) `C_p-C_v` =R
d) `triangleU = C_vdT` for all processes

A

a,c,d

B

b,c,d,

C

c,d

D

a,c

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the properties of an ideal gas, we will analyze each statement one by one. ### Step 1: Analyze Statement A **Statement A:** U & H depend only on temperature. - **Explanation:** For an ideal gas, the internal energy (U) and enthalpy (H) are functions of temperature only. This is because the internal energy of an ideal gas is related to the kinetic energy of the gas molecules, which depends solely on temperature. Similarly, enthalpy is also a function of temperature for an ideal gas. - **Conclusion:** This statement is **true**. ### Step 2: Analyze Statement B **Statement B:** Compressibility factor (Z) cannot be 1. - **Explanation:** The compressibility factor (Z) is defined as Z = PV/RT. For an ideal gas, this relationship holds true, and thus Z = 1. Therefore, it is incorrect to state that the compressibility factor cannot be 1 for an ideal gas. - **Conclusion:** This statement is **false**. ### Step 3: Analyze Statement C **Statement C:** \( C_p - C_v = R \) - **Explanation:** For an ideal gas, the difference between the heat capacities at constant pressure (C_p) and constant volume (C_v) is equal to the gas constant R. This is a fundamental relationship in thermodynamics for ideal gases. - **Conclusion:** This statement is **true**. ### Step 4: Analyze Statement D **Statement D:** \( \Delta U = C_v dT \) for all processes. - **Explanation:** The equation \( \Delta U = C_v dT \) is valid for processes where the heat capacity at constant volume (C_v) is applicable, such as in a constant volume process. However, this relationship does not hold true for processes that are not at constant volume (e.g., isothermal processes). Therefore, it is not universally applicable to all processes. - **Conclusion:** This statement is **false**. ### Final Conclusion From the analysis: - Statement A is true. - Statement B is false. - Statement C is true. - Statement D is false. Thus, the true statements for one mole of an ideal gas are A and C. ### Summary of Answers: - A: True - B: False - C: True - D: False
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