The maximum amount of work done, which can be obtained by supplying 400 cal of heat will be

Options

A. 1 kJ
B. 1.2 kJ
C. `1.76kJ`
D. `1.68kJ`

Answer

To solve the problem of finding the maximum amount of work done when 400 cal of heat is supplied, we can use the concept of efficiency in thermodynamics. Here’s a step-by-step solution:

### Step 1: Understand the relationship between heat and work
In thermodynamics, the maximum work done (W) can be derived from the heat supplied (Q) using the efficiency (η) of the process. The efficiency is defined as:
\[ \eta = \frac{W}{Q} \]
For a reversible process, the maximum efficiency is given by the Carnot efficiency, which is dependent on the temperatures of the heat reservoirs.

### Step 2: Convert calories to joules
Since the problem states that 400 cal of heat is supplied, we need to convert this to joules because the standard unit of energy in the SI system is joules. The conversion factor is:
\[ 1 \text{ cal} = 4.184 \text{ J} \]
Thus, we can convert 400 cal to joules:
\[ Q = 400 \text{ cal} \times 4.184 \text{ J/cal} = 1673.6 \text{ J} \]

### Step 3: Calculate the maximum work done
For maximum work done, we can assume that the efficiency (η) is 1 (100%) for a reversible process. Therefore, the maximum work done (W) will be equal to the heat supplied (Q):
\[ W = Q = 1673.6 \text{ J} \]

### Step 4: Convert work done back to kilocalories if needed
If we want to express the work done in kilocalories, we can convert joules back to kilocalories using the conversion:
\[ 1 \text{ kcal} = 4184 \text{ J} \]
Thus, converting joules to kilocalories:
\[ W = \frac{1673.6 \text{ J}}{4184 \text{ J/kcal}} \approx 0.4 \text{ kcal} \]

### Final Answer
The maximum amount of work done which can be obtained by supplying 400 cal of heat is approximately **0.4 kcal** or **1673.6 J**.

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