A gas absorbs `100 Calorie` of heat and performs `150J` of work. Increase energy of the gas in the process is

Options

A. `420J`
B. `570J`
C. `270J`
D. none of these

Explanation

To find the increase in the internal energy of the gas, we can use the first law of thermodynamics, which states:

\[ \Delta U = Q - W \]

where:
- \(\Delta U\) is the change in internal energy,
- \(Q\) is the heat absorbed by the system,
- \(W\) is the work done by the system.

### Step 1: Convert heat from calories to joules
The heat absorbed by the gas is given as \(100 \text{ Cal}\). We need to convert this to joules using the conversion factor \(1 \text{ Cal} = 4.2 \text{ J}\).

\[ Q = 100 \text{ Cal} \times 4.2 \text{ J/Cal} = 420 \text{ J} \]

### Step 2: Identify the work done
The work done by the gas is given as \(150 \text{ J}\).

\[ W = 150 \text{ J} \]

### Step 3: Apply the first law of thermodynamics
Now, we can substitute the values of \(Q\) and \(W\) into the first law equation to find \(\Delta U\).

\[ \Delta U = Q - W \]
\[ \Delta U = 420 \text{ J} - 150 \text{ J} \]

### Step 4: Calculate the change in internal energy
Now, perform the subtraction:

\[ \Delta U = 270 \text{ J} \]

Thus, the increase in the internal energy of the gas is \(270 \text{ J}\).

### Final Answer:
The increase in energy of the gas in the process is \(270 \text{ J}\).

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