When determining the specific heat from a given metal in a calorimeter the mass of the water remains constant, but the mass of the metal is increased what would happen to the equilibrium temperature? Explain your choice.
Wondering which is hotter to begin, the metal or the water?
it didn't say!
When the mass of the metal in a calorimeter is increased while the mass of water remains constant, the equilibrium temperature would decrease. This can be explained by the principle of heat transfer and the equation for thermal equilibrium.
The principle of heat transfer states that heat always flows from a higher temperature object to a lower temperature object until they reach thermal equilibrium. In this case, the metal and water are initially at different temperatures, and heat flows from the hotter object (the metal) to the cooler object (the water) until they reach the same temperature.
The equation for thermal equilibrium is:
m1c1ΔT1 = m2c2ΔT2
where:
m1 = mass of the metal
c1 = specific heat of the metal
ΔT1 = change in temperature of the metal
m2 = mass of the water
c2 = specific heat of the water
ΔT2 = change in temperature of the water
Assuming ΔT1 and ΔT2 are equal since they reach thermal equilibrium, we can rearrange the equation as:
(m1c1) / (m2c2) = 1
Now, if the mass of the metal (m1) increases while the mass of the water (m2) remains constant, the ratio (m1/m2) increases. Since the ratio on the left side of the equation is now larger, the specific heat of the metal (c1) needs to decrease to maintain the equality in the equation.
Specific heat is a material property that indicates how much heat energy is required to raise the temperature of a substance. Therefore, when the specific heat of the metal decreases, it means the metal can actually transfer more heat energy to the water compared to before. As a result, the equilibrium temperature will be lower since more heat can be transferred from the metal to the constant mass of water.
The equilibrium temperature in a calorimeter is the final temperature achieved when the metal and the water reach thermal equilibrium. When determining the specific heat of a metal, it is necessary to measure the heat gained or lost by both the metal and the water. The equation used to calculate the specific heat is:
Q = m * c * ΔT
where:
Q is the heat gained or lost by the substance,
m is the mass of the substance,
c is the specific heat of the substance, and
ΔT is the change in temperature.
In this case, the mass of the water remains constant, meaning its heat gained or lost (Q_w) is the same. We can assume that the heat gained by the water is equal to the heat lost by the metal:
Q_w = Q_m
The equation can be rearranged to solve for the change in temperature:
m_w * c_w * ΔT_w = m_m * c_m * ΔT_m
where:
m_w is the mass of the water,
c_w is the specific heat of the water,
ΔT_w is the change in temperature of the water,
m_m is the mass of the metal,
c_m is the specific heat of the metal, and
ΔT_m is the change in temperature of the metal.
If the mass of the metal is increased, the term m_m * c_m in the equation will also be increased. Since Q_w is constant, to maintain equilibrium, ΔT_m must decrease.
Therefore, when the mass of the metal is increased, the equilibrium temperature (ΔT_m) will decrease.