Question

The uncertainty in the values for specific heat capacity is 5%. Water of mass (100+-2) g is heated from (75.0+_0.5)C to (85.0+-0.5)C. (i) Calculate the energy required to raise the temperature of the water from 75C to 85C.?

Answer 1

`(4186 +- 3.68)\ "J"`

Explanation:

Energy (`"Q"`) required to raise the temperature is given as

`"Q = mSΔT"`

Where

• `"m ="` Mass of sample
• `"S ="` Specific heat capacity of sample (`"4.186 J/g°C"` for water)
• `"ΔT ="` Change in temperature of sample

`"Q" = 100 cancel"g" × 4.186\ "J"/(cancel"g" cancel"°C") × (85 - 75)\ cancel"°C" = 4186\ "J"`

It’s given that

`(Δ"S")/("S") × 100 = 5`

`"ΔS"/"S" = 5/100`

Now, from the formula `"Q = mS(T"_f - "T"_i")"`

`"ΔQ"/"Q" = ["Δm"/"m" + "ΔS"/"S"]["ΔT"_f/"T"_f + "ΔT"_i/"T"_i]`

`"ΔQ" = "4186 J"[2/100 + 5/100][0.5/85 + 0.5/75] = "3.68 J"`

∴ Energy required is `(4186 +- 3.68)\ "J"`