when exposed to the same amount of heat for the same amount of time, a 3 g sample of copper will experience a greater temperature change then a 12 g sample of copper due to its smaller what?
Mass
When a substance is heated, it absorbs thermal energy, which increases its temperature. The amount of temperature change experienced by a substance depends on its specific heat capacity.
To answer this question, we need to understand that specific heat capacity is a property that determines how much heat energy is required to raise the temperature of a given amount of a substance by a certain degree. This property is unique to each substance.
To find the specific heat capacity, we use the equation:
Q = mcΔT
Where:
Q is the heat energy absorbed or released,
m is the mass of the substance,
c is the specific heat capacity, and
ΔT is the change in temperature.
Given that both samples of copper are exposed to the same amount of heat for the same amount of time, the heat energy absorbed (Q) is constant. Let's assume the value of Q is the same for both samples.
In this case, we can set up a ratio to compare the temperature change (ΔT) for the two samples:
m₁c₁ΔT₁ = m₂c₂ΔT₂
Where:
m₁ and m₂ are the masses of the two copper samples, and
c₁ and c₂ are the specific heat capacities of copper.
We are given that the mass of the smaller sample (m₁) is 3 g and the mass of the larger sample (m₂) is 12 g. We are also told that both samples are made of copper, so the specific heat capacities (c₁ and c₂) are the same.
Since both samples are exposed to the same amount of heat for the same amount of time, the heat energy absorbed (Q) is the same. Therefore, we can write:
m₁ΔT₁ = m₂ΔT₂
Now, we can compare the temperature change by setting up the ratio of the masses:
m₁/m₂ = 3 g / 12 g
Simplifying, we find:
1/4 = 3/12
To make the comparison clearer, we can multiply both sides of the equation by 4:
(1/4) * 4 = (3/12) * 4
1 = 3/3
1 = 1
Since both sides of the equation are equal, the temperature change (ΔT) for both samples of copper will be the same when exposed to the same amount of heat for the same amount of time. Therefore, the initial statement is incorrect.
In conclusion, the 3 g sample of copper will not experience a greater temperature change compared to the 12 g sample of copper when exposed to the same amount of heat for the same amount of time.
mass
heat in = specific heat * mass * temperature rise