Question

How many joules are required to heat up a cup of water from 14.5°c to 99.0°c? 1cup=8ounces;1ounce=29.573ml;DH2O at 14.5°c=0.999174g/ml.can anyone help please and thank you.

Answer 1

You must supply 83.6 kJ.

Explanation:

The formula for the quantity of heat `q` transferred is

`color(blue)(bar(ul(|color(white)(a/a)q = mC_text(s)ΔTcolor(white)(a/a)|)))" "`

where

`m color(white)(ll) =` the mass of the object
`C_text(s) color(white)(l) =` its specific heat capacity
`ΔT =` its change in temperature

In this problem,

`C_text(s) color(white)(ll)= "4.184 J·°C"^"-1""g"^"-1"`
`ΔT = T_text(f) - T_text(i) = "99.0 °C - 14.5 °C = 84.5 °C"`

Your first task is to find the mass of the water.

`m = 1 color(red)(cancel(color(black)("cup"))) × (8 color(red)(cancel(color(black)("oz"))))/(1 color(red)(cancel(color(black)("cup")))) × (29.573 color(red)(cancel(color(black)("mL"))))/(1 color(red)(cancel(color(black)("oz")))) × "0.999 174 g"/(1 color(red)(cancel(color(black)("mL")))) = "236 g"`

Now you can determine the quantity of heat needed.

`q = 236 "g" × 4.184 "J"·color(red)(cancel(color(black)("°C"^"-1""g"^"-1"))) × 84.5 color(red)(cancel(color(black)("°C"))) = "83 600"color(white)(l)"J" = "83.6 kJ"`