The temperature of a sample of water changes from 10°C to 20°C when the water absorbs 420 joules of heat. What is the mass of the sample?

Question

Natalie Anton · Accepted Answer

#10.03# grams

The following formula can be used to solve the issue: #Q=mCpDeltaT# where #Q=heat# #m=mass# #Cp=sp. heat# #DeltaT=temperature# change #(T_2-T_1)# Some data are provided in the problem like #Q=420# Joules #T_2=20^oC# #T_1=10^oC# and the ##[specific heat](https://tutor.hix.ai) of water is known to be #4.186 (J)/(g.^oC)#. (https://tutor.hix.ai) All you have to do is to rearrange the original formula to isolate #m# and to derive the new formula which is; #m=(Q)/(CpDeltaT)#, plug in values and make sure to cancel out units. until you have the desired unit.

Jeremiah Adams · Answer

undefined To find the mass of the sample of water, we can use the specific heat capacity formula:

$$Q = mcΔT$$

Where:
- $Q$ = heat energy absorbed (in joules)
- $m$ = mass of the sample (in grams)
- $c$ = specific heat capacity of water (4.18 J/g°C)
- $ΔT$ = change in temperature (in °C)

Given that $Q = 420$ J, $ΔT = 20 - 10 = 10°C$, and $c = 4.18$ J/g°C, we can rearrange the formula to solve for $m$:

$$m = \frac{Q}{cΔT}$$

$$m = \frac{420}{4.18 \times 10}$$

$$m = \frac{420}{41.8}$$

$$m ≈ 10.05 \text{ grams}$$

So, the mass of the sample of water is approximately 10.05 grams.