When temperature of a gas is increased then which of the following statements is always true ?

Options

A. work done of the gas
B. Heat is supplied to gas
C. Internal energy of gas is increased
D. pressure of gas remains unchanged.

Explanation

To determine which statement is always true when the temperature of a gas is increased, we can analyze the properties of gases based on the kinetic theory and thermodynamics. Here’s a step-by-step solution:

### Step 1: Understand the Relationship Between Temperature and Kinetic Energy
- According to the kinetic theory of gases, the temperature of a gas is directly related to the average kinetic energy of its molecules. The equation for the average kinetic energy (KE) of gas molecules is given by:
\[ KE = \frac{3}{2} k T \]
where \( k \) is the Boltzmann constant and \( T \) is the temperature in Kelvin.

### Step 2: Analyze the Effect of Temperature Increase
- When the temperature of the gas increases, the average kinetic energy of the molecules also increases. This means that the molecules move faster and collide more energetically.

### Step 3: Consider Internal Energy
- The internal energy (U) of an ideal gas is also a function of temperature. For an ideal gas, the internal energy can be expressed as:
\[ U = nC_vT \]
where \( n \) is the number of moles, \( C_v \) is the molar heat capacity at constant volume, and \( T \) is the temperature. Thus, when the temperature increases, the internal energy also increases.

### Step 4: Evaluate Work Done and Heat
- Work done (W) by the gas is not directly related to temperature. It depends on the process the gas undergoes (e.g., isothermal, adiabatic). Therefore, we cannot conclude that work done will always increase with temperature.
- Similarly, heat (Q) added to the system can vary based on the specific process and is not solely dependent on temperature.

### Conclusion
- From the analysis, we can conclude that the statement that is always true when the temperature of a gas is increased is:
**The internal energy of the gas increases.**

### Summary of Steps:
1. Recognize the relationship between temperature and kinetic energy.
2. Understand that increasing temperature leads to increased kinetic energy.
3. Acknowledge that internal energy is a function of temperature and increases with temperature.
4. Note that work done and heat are not directly related to temperature changes.