Question
If you have two substances of equal mass that have their temperature increased by 10 degrees C each,
but one of the substances requires twice as much heat as the other to have this temperature change,
what can you claim about the two objects?
Answers below:
One object has twice as much mass as the other object
One object has twice the specific heat capacity of the other object
Both objects received the same amount of heat
One object is solid, the other is liquid
but one of the substances requires twice as much heat as the other to have this temperature change,
what can you claim about the two objects?
Answers below:
One object has twice as much mass as the other object
One object has twice the specific heat capacity of the other object
Both objects received the same amount of heat
One object is solid, the other is liquid
Answers
Answered by
GPT-4o mini
To analyze the situation, let's recall the formula for heat transfer:
\[ Q = mc\Delta T \]
Where:
- \( Q \) is the heat added or removed,
- \( m \) is the mass of the substance,
- \( c \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.
Given that the two substances have equal mass (let's denote the mass as \( m \)) and both are heated by the same temperature change of \( \Delta T = 10 \) degrees C, we can express the heat required for each substance as follows:
- For Substance 1 (which requires heat \( Q_1 \)):
\[ Q_1 = mc_1 \Delta T \]
- For Substance 2 (which requires heat \( Q_2 \)):
\[ Q_2 = mc_2 \Delta T \]
According to the problem, one substance (let's say Substance 2) requires twice as much heat as Substance 1:
\[ Q_2 = 2Q_1 \]
Substituting the expressions for \( Q_1 \) and \( Q_2 \):
\[ mc_2 \Delta T = 2(mc_1 \Delta T) \]
Since both substances have the same mass \( m \) and experience the same temperature change \( \Delta T \), we can simplify:
\[ c_2 = 2c_1 \]
This means that Substance 2 has twice the specific heat capacity of Substance 1.
Based on this analysis, the correct statement is:
**One object has twice the specific heat capacity of the other object.**
\[ Q = mc\Delta T \]
Where:
- \( Q \) is the heat added or removed,
- \( m \) is the mass of the substance,
- \( c \) is the specific heat capacity,
- \( \Delta T \) is the change in temperature.
Given that the two substances have equal mass (let's denote the mass as \( m \)) and both are heated by the same temperature change of \( \Delta T = 10 \) degrees C, we can express the heat required for each substance as follows:
- For Substance 1 (which requires heat \( Q_1 \)):
\[ Q_1 = mc_1 \Delta T \]
- For Substance 2 (which requires heat \( Q_2 \)):
\[ Q_2 = mc_2 \Delta T \]
According to the problem, one substance (let's say Substance 2) requires twice as much heat as Substance 1:
\[ Q_2 = 2Q_1 \]
Substituting the expressions for \( Q_1 \) and \( Q_2 \):
\[ mc_2 \Delta T = 2(mc_1 \Delta T) \]
Since both substances have the same mass \( m \) and experience the same temperature change \( \Delta T \), we can simplify:
\[ c_2 = 2c_1 \]
This means that Substance 2 has twice the specific heat capacity of Substance 1.
Based on this analysis, the correct statement is:
**One object has twice the specific heat capacity of the other object.**