The behaviour of ideal gas is goverened by various gas laws which are described by mathematical statements as given below:
(`i`) `PV=k` (constant) at constant `n` and `T`
(`ii`) `V//T=k_(2)` (constant) at constant `n` and `P`
(`iii`) `V//n=k_(3)` (constant) at constant `T` and `P`
(`iv`) `PV=nRT`
(`v`) `P//T=k_(4) (constant) at constant `n` and `V`
Answer the following
The value of `k_(2)` is

Options

A. Independent of nature and amount of gas
B. Depends on temperature and pressure conditions
C. Depends on pressure and amount of gas
D. Depends only on nature of gas

Explanation

To find the value of \( k_2 \) from the given gas laws, we can follow these steps:

### Step 1: Understand the relationship given by the gas laws
We are provided with the equation \( \frac{V}{T} = k_2 \) at constant \( n \) (number of moles) and \( P \) (pressure). This indicates that the volume \( V \) of an ideal gas is directly proportional to its temperature \( T \) when the amount of gas and pressure are held constant.

### Step 2: Use the Ideal Gas Law
The Ideal Gas Law is given by:
\[
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