# Specific heat mixture, final temp, etc.

• 1MileCrash
In summary, specific heat is the amount of heat needed to raise the temperature of a substance by one degree, and the specific heat of a mixture is the weighted average of the individual substances. To calculate the final temperature of a mixture, the formula Tf = (m1c1T1 + m2c2T2 + ... + mncnTn) / (m1c1 + m2c2 + ... + mncn) can be used. Specific heat is an intrinsic property while heat capacity is an extrinsic property that depends on the mass of the substance. The higher the specific heat of a substance, the more heat is needed to change its temperature, resulting in a smaller temperature change compared to substances with lower

## Homework Statement

The specific heat of lead is 0.03 cal/g*C. 300 grams of lead shot at 100* C is mixed with 100 grams of water at 70* C. What is the final temperature of the mixture if the container is insulated.

## The Attempt at a Solution

Q1 = c1m1(Tf - 100) (lead)
Q2 = c2m2(Tf - 70) (water)

Q1 + Q2 = 0

c1m1(Tf - 100) + c2m2(Tf - 70) = 0
9(Tf - 100) + 100(Tf - 70) = 0
9Tf - 900 + 100Tf - 700 = 0
109Tf = 1600
Tf = 14.7*C = no

EDIT, nevermind... 100 x 70 = 700, you heard it here first!

Last edited:
100 x 70 ≠ 700

gneill said:
100 x 70 ≠ 700

I caught it.

Works out fine now. Thanks!

## What is specific heat?

Specific heat is the amount of heat required to raise the temperature of one gram of a substance by one degree Celsius or Kelvin.

## What is the specific heat of a mixture?

The specific heat of a mixture is the weighted average of the specific heats of the individual substances in the mixture.

## How do you calculate the final temperature of a mixture?

The final temperature of a mixture can be calculated using the formula: Tf = (m1c1T1 + m2c2T2 + ... + mncnTn) / (m1c1 + m2c2 + ... + mncn),where Tf is the final temperature, m is the mass of each substance, c is the specific heat of each substance, and T is the initial temperature of each substance.

## What is the difference between specific heat and heat capacity?

Specific heat is an intrinsic property of a substance, while heat capacity is an extrinsic property that depends on the mass of the substance. Specific heat is expressed in J/g·K, while heat capacity is expressed in J/K.

## How does specific heat affect the temperature change of a substance?

The higher the specific heat of a substance, the more heat is required to increase its temperature. This means that substances with higher specific heats will have a smaller temperature change compared to substances with lower specific heats when the same amount of heat is added or removed.