The specific heat capacity of liquid mercury is 0.14 J/g°C. How many joules of heat are needed to raise the temperature of 2.50 kg of mercury from 309 K to 311 K? a. -700 J b. 800 J c. -600 J d. 600 J e. 700 J
The Correct Answer and Explanation is:
To solve this problem, we use the formula for heat energy:q=mcΔTq = mc\Delta Tq=mcΔT
Where:
- qqq is the heat energy in joules
- mmm is the mass of the substance
- ccc is the specific heat capacity
- ΔT\Delta TΔT is the change in temperature
Step 1: Convert mass to grams
The specific heat capacity is given in J/g°C, so we need the mass in grams.2.50 kg=2500 g2.50 \, \text{kg} = 2500 \, \text{g}2.50kg=2500g
Step 2: Calculate the temperature change
ΔT=Tfinal−Tinitial=311 K−309 K=2 K\Delta T = T_{\text{final}} – T_{\text{initial}} = 311\,\text{K} – 309\,\text{K} = 2\,\text{K}ΔT=Tfinal−Tinitial=311K−309K=2K
Since we are dealing with a temperature difference, a change of 1 Kelvin is equal to a change of 1°C, so we can treat the temperature change as 2°C.
Step 3: Use the specific heat formula
q=(2500 g)×(0.14 J/g°C)×(2 °C)=700 Jq = (2500 \, \text{g}) \times (0.14 \, \text{J/g°C}) \times (2 \, \text{°C}) = 700 \, \text{J}q=(2500g)×(0.14J/g°C)×(2°C)=700J
Final Answer:
e. 700 J
Explanation:
This problem tests your understanding of how heat energy is related to mass, specific heat capacity, and temperature change. Specific heat capacity is a material-specific constant that tells us how much energy is needed to raise the temperature of 1 gram of a substance by 1 degree Celsius. Mercury has a low specific heat capacity compared to water, meaning it heats up and cools down more quickly.
Here, we are heating 2.5 kg (2500 g) of liquid mercury by 2 degrees Celsius. The specific heat capacity of mercury is 0.14 J/g°C. Multiplying the mass, specific heat, and temperature change gives us the energy required in joules. The answer is positive because energy is being added to raise the temperature. Therefore, the correct answer is 700 J.
