Heat Loss Question: Single Coin vs All Coins

[twilos]

Homework Statement

A stack of identical coins is all at a temperature of 100 C. The coins are transferred to a container of room temperature water. After thermal equilibrium is reached the final temperature is 35 C. The Heat lost by a single coin is less/greater/equal to the heat lost by all the coins?

Homework Equations

Q=mc(Change)T

The Attempt at a Solution

I believe the heat lost by one single coin will be equal to the heat lost by all of the coins but I am unsure. If you think about it, the stack of coins are all the same and if you compare one coin's heat lost to the heat loss by all the of the same coin wouldn't it be the same.

But also if you think about it another way the heat lost of one coin has to be less than the heat lost of all because its one vs a whole system...

Some clarification would be awesome thanks!

 

[visharad]

For a single coin, it will be less.
Q = m * c * deltaT
c is specific heat capacity of the material of coin (e.g. copper or anything of which the coins are made). This is same for all coins.
deltaT is also same because T changes from 100 deg C to 35 deg C for all coins.

m for single coin is less than m for all coins. So Q will be smaller for single coin.

Another way to look at it:-
Coins are initially at 100 deg C. Then they are put in a room and at equilibrium, the temperature is 25 deg C.
This means the coins lose heat and surrounding gains heat. Let Q = heat gained by surroundings. Then Q = heat lost by all coins.
Q is the total heat lost by all coins. Therefore one coin will lose less heat than Q.

 

[thomate1]

I would like to point out that the heat lost by a single coin and the heat lost by all the coins are not directly comparable in this scenario. This is because the heat lost by a single coin is only a fraction of the total heat lost by the entire stack of coins.

To determine the heat lost by a single coin, we would need to know the specific heat capacity of the coin and its mass. From there, we could use the equation Q=mcΔT to calculate the heat lost. However, the heat lost by all the coins would be the sum of the heat lost by each individual coin, which would be a larger value.

In this scenario, it is more accurate to say that the heat lost by a single coin is equal to the average heat lost by each individual coin in the stack. This is because the coins are all at the same initial temperature and are transferred to the same container of water, so the temperature change and specific heat capacity would be the same for each coin.

Overall, it is important to consider the specific conditions and variables in a situation before making direct comparisons between quantities. In this case, the heat lost by a single coin and the heat lost by all the coins are not directly comparable.