How Well Do You Know About Heat Capacity? Let's Test Your Knowledge!

What is the heat capacity of the unknown substance?

Given data: A 2.62g sample of a substance suspected of being pure gold is warmed to 72.3∘C and submerged into 15.6g of water initially at 24.8∘C. The final temperature of the mixture is 26.0∘C.

Choose one:

  • A. 0.031 cal/g.°C
  • B. 0.028 cal/g.°C
  • C. 0.026 cal/g.°C
  • D. 0.034 cal/g.°C

Answer:

The correct answer is A. 0.031 cal/g.°C

Heat capacity can be determined by using the formula q=mcΔT, where q is the heat transfer, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

  1. First we calculate the heat gained by water using the formula q = mcΔT (m represents the mass of water, c is the specific heat capacity of water, ΔT is the change in water temperature). So q_water = 15.6 * 1 (assuming that the specific heat capacity of water is 1) * (26.0-24.8) = 18.72 cal.
  2. As per the law of energy conservation, the heat lost by gold equals the heat gained by the water, hence q_gold = - q_water = -18.72 cal.
  3. Now, we can find the specific heat capacity of the substance (gold) using the same formula (q = mcΔT). Therefore, c_gold = q_gold / (m_gold * ΔT_gold) = -18.72 cal / (2.62 g * (26-72.3)) = 0.031 cal/g.°C.
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