Given that, for first condition,
Initial temperature,
T1=52.5°C Final temperature,
Tv=47.5°C Average temperature,
Tav= ==50°C For second condition,
Initial temperature,
T1=47.5°C Final temperature,
T2=42.5°C Average temperature,
Tav= ==45°C Let
T0 be the temperature of surroundings.
Now, using expression of rate of cooling,
R==−K(Tav−T0) Substituting the values in above equation from
1‌st and 2nd conditions, we get
=−K(Tav−T0) =−K(50−T0) ...(i)
Similarly,
=−K(45−T0) ...(ii)
Dividing Eq. (i) by Eq. (ii), we get
=| −K(50−T0) |
| −K(45−T0) |
⇒×= ⇒= T0=35°C Hence, the temperature of surroundings is
35°C.