## Another 8.41 Question

Grace Ramey 2K
Posts: 57
Joined: Thu Jul 27, 2017 3:01 am

### Another 8.41 Question

I have a follow-up question for 8.41:

The solutions manual, when setting the heat change of the ice cube and the heat change of the water equal, puts a negative sign in front of the heat change for the water (which is on the left side of the equals sign in the equation below). The equation comes out looking like this (Tf = final temperature):

-(1.67x10^3 J/°C)(Tf) + 7.5x10^4 J = 1.67x10^4 J + (209 J/°C)(Tf)

Can someone explain that negative sign to me? The only thing I can think of is that it is made negative because the water loses heat, but I am not sure about this.

Ethan-Van To Dis2L
Posts: 50
Joined: Fri Sep 29, 2017 7:05 am

### Re: Another 8.41 Question

Essentially yes. The negative sign is due to the loss of heat in the water, and then that heat enters the ice. Think of it as two systems. The heat leaves one system (negative sign) to enter another (positive sign)

Seth_Evasco1L
Posts: 54
Joined: Thu Jul 27, 2017 3:00 am

### Re: Another 8.41 Question

You can think of the ice cube as the system and the water as the surroundings. In relation to the system, the system is gaining heat (positive) and the surroundings are losing heat (negative). The heat transfer is from the surroundings to the system.

Krupa Prajapati
Posts: 50
Joined: Sat Jul 22, 2017 3:00 am

### Re: Another 8.41 Question

Hi Grace,

Since q simply represents the amount of heat transferred to a system, q ice = -q water. The ice, the system, is gaining heat while the water, the surrounding, is loosing the same amount of heat. Therefore, when we substitute q for m*c*(t final - t initial) we put a negative in front of the q value for water. Hope this helps!