Answer
(a) +27.2$^{\circ}$C
(b) -55.6$^{\circ}$C
Work Step by Step
(a) The initial temperature is -4.0$^{\circ}$F and the final temperature is 45.0$^{\circ}$F.
The problem asked for the temperature change in Celsius degrees. First, we'll convert the initial temperature to Celsius.
$$T_{c} = \frac{5}{9} (T_{f} - 32)$$
$$T_{c} = \frac{5}{9} (-4.0 - 32)$$
$$T_{c} = -20^{\circ}C$$
Next, we'll convert the final temperature to Celsius.
$$T_{c} = \frac{5}{9} (T_{f} - 32)$$
$$T_{c} = \frac{5}{9} (45.0 - 32)$$
$$T_{c} = 7.2^{\circ}C$$
Now, just subtract the initial temperature in celsius from the final temperature in celsius to get the change in temperature in celsius.
$$\Delta T = T_{f} - T_{i}$$
$$\Delta T = 7.2^{\circ}C - (-20)^{\circ}C$$
$$\Delta T = 27.2^{\circ}C$$
(b) The initial temperature is 44.0$^{\circ}$F and the final temperature is -56$^{\circ}$F.
The problem asked for the temperature change in Celsius degrees. First, we'll convert the initial temperature to Celsius.
$$T_{c} = \frac{5}{9} (T_{f} - 32)$$
$$T_{c} = \frac{5}{9} (44.0 - 32)$$
$$T_{c} = 6.7^{\circ}C$$
Next, we'll convert the final temperature to Celsius.
$$T_{c} = \frac{5}{9} (T_{f} - 32)$$
$$T_{c} = \frac{5}{9} ((-56) - 32)$$
$$T_{c} = -48.9^{\circ}C$$
Now, just subtract the initial temperature in celsius from the final temperature in celsius to get the change in temperature in celsius.
$$\Delta T = T_{f} - T_{i}$$
$$\Delta T = (-48.9)^{\circ}C - 6.7^{\circ}C$$
$$\Delta T = -55.6^{\circ}C$$
