How many joules are required to heat 15.2 g of water at 35.0°C to 70.0°C?

1 Answer
Dec 14, 2015

Answer:

#"2,220 J"#

Explanation:

In order to be able to determine how much heat is required to increase the temperature of your sample of water from #35.0^@"C"# to #70.0^@"C"#, you need to know the value of water's specific heat.

As you know, a substance's specific heat tells you how much heat is required to increase the temperature of #"1 g"# of that substance by #1^@"C"#.

Water has a specific heat of about #4.18 "J"/("g" ""^@"C")#. This tells you that in order to increase the temperature of #"1 g"# of water by #1^@"C"#, you need to provide it with #"4.18 J"# of heat.

Now, here's how you can think about what's going on here. in order to increase the temperature of #"4.18 g"# of water by #1^@"C"#, you would need #4.18# times more heat than water's specific heat value.

Likewise, in order to increase the temperature of #"4.18 g"# of water by #4.18^@"C"#, you'd need #(4.18 xx 4.18)# times more heat than water's specific heat value.

In your case, you need to increase the temperature of #"15.2 g"# of water by #35.0^@"C"#, which tells you that you're going to need #(15.2 xx 35)# times more heat than water's specific heat value.

Mathematically, this is expressed as

#color(blue)(q = m * c * DeltaT)" "#, where

#q# - heat absorbed/lost
#m# - the mass of the sample
#c# - the specific heat of the substance
#DeltaT# - the change in temperature, defined as final temperature minus initial temperature

Plug in your values to get

#q = 15.2 color(red)(cancel(color(black)("g"))) * 4.18"J"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * (70.0 - 35.0)color(red)(cancel(color(black)(""^@"C")))#

#q = "2223.76 J"#

Rounded to three sig figs, the answer will be

#q = color(green)("2,220 J")#