Two bodies A and B have the same mass and receive the same amount of heat. If the temperature of A rises more than that of B due to this heating, what can you conclude about their specific heat capacities?

Introduction / Context:
Specific heat capacity tells us how much heat is needed to raise the temperature of a unit mass of a substance by one degree. When equal amounts of heat are supplied to equal masses of different substances, they generally show different temperature rises depending on their specific heat capacities. This question uses that idea to compare two bodies A and B when A shows a larger temperature rise than B for the same supplied heat and equal mass.

Given Data / Assumptions:

• Bodies A and B have the same mass m.
• The same amount of heat Q is given to both bodies.
• The temperature rise of A is larger than the temperature rise of B.
• We assume no heat loss to surroundings, so all supplied heat goes into raising temperatures.
• We neglect phase changes or chemical reactions.

Concept / Approach:
The relation between heat, specific heat capacity and temperature change is Q = m * c * delta T, where m is mass, c is specific heat capacity and delta T is temperature change. For given Q and m, the temperature rise delta T is inversely proportional to c. A substance with a lower specific heat capacity will have a larger temperature rise for the same heat input. Since A shows a greater temperature increase than B while having the same mass and receiving the same heat, it must have a smaller specific heat capacity than B.

Step-by-Step Solution:
Step 1: Write the heating equation for body A: Q = m * cA * delta TA. Step 2: Write the heating equation for body B: Q = m * cB * delta TB. Step 3: Since Q and m are the same for both bodies, divide the two equations to obtain cA * delta TA equals cB * delta TB. Step 4: Rearrange to get cA divided by cB equals delta TB divided by delta TA. Step 5: Because delta TA is greater than delta TB, the ratio delta TB divided by delta TA is less than one, so cA is less than cB, meaning body A has smaller specific heat capacity than body B.

Verification / Alternative check:
Consider a simple numerical example. Take equal masses of water and copper. Water has a large specific heat, while copper has a much smaller one. If you supply the same amount of heat to both equal masses, copper temperature rises more than the water temperature. This real life example follows exactly the pattern given in the question and fits the conclusion that the body showing larger temperature increase has lower specific heat capacity. This supports the reasoning that cA is less than cB.

Why Other Options Are Wrong:
The specific heat capacity of A is greater than that of B would make delta TA smaller than delta TB for the same Q and m, opposite to what is described.
Options suggesting both A and B have the same specific heat capacity rely on thermal conductivity, which affects rate of heat flow, not the final temperature rise for a fixed amount of heat absorbed.
Specific heat capacities of both must be zero is impossible, since then any finite heat would cause infinite temperature change, which does not match observation.

Common Pitfalls:
Students sometimes confuse thermal conductivity, which controls how fast heat flows through a material, with specific heat capacity, which controls how much heat is needed to change temperature. The question concerns final temperature rise for given heat input, where conductivity does not matter if each body is heated uniformly. Another mistake is to reason qualitatively without using the simple formula Q = m * c * delta T, which immediately clarifies the inverse relationship between specific heat capacity and temperature rise.

Final Answer:
Since body A warms more for the same heat and mass, the specific heat capacity of A is less than that of B.