Question

perform the following temperature conversions. use appropriate signi
to convert °c to k: \t\tt_k = t_°c + 273.15
to convert k to °c: \t\tt_°c = t_k - 273.15
to convert °c to °f: \t\tt_°f = 1.8(t_°c) + 32
to convert °f to °c: \t\tt_°c = (t_°f - 32)/1.8

1. 75°c = \boxed{} k
2. 290 k = \boxed{} °c
3. 24.0°c = \boxed{} k
4. 85.0°f = \boxed{} °c
5. 12°c = \boxed{} °f
6. 101°c = \boxed{} °f
7. 75°f = \boxed{} °c
8. 64°f = \boxed{} k
9. 320 k = \boxed{} °f
10. 36°f = \boxed{} k
11. 298 k = \boxed{} °f

Explanation:

Step1: Convert 75°C to K

Use \( T_K = T_{^\circ\text{C}} + 273.15 \): \( 75 + 273.15 = 348.15 \)

Step2: Convert 290 K to °C

Use \( T_{^\circ\text{C}} = T_K - 273.15 \): \( 290 - 273.15 = 16.85 \)

Step3: Convert 24.0°C to K

Use \( T_K = T_{^\circ\text{C}} + 273.15 \): \( 24.0 + 273.15 = 297.15 \)

Step4: Convert 85.0°F to °C

Use \( T_{^\circ\text{C}} = (T_{^\circ\text{F}} - 32)/1.8 \): \( (85.0 - 32)/1.8 ≈ 29.44 \)

Step5: Convert 12°C to °F

Use \( T_{^\circ\text{F}} = 1.8(T_{^\circ\text{C}}) + 32 \): \( 1.8×12 + 32 = 53.6 \)

Step6: Convert 101°C to °F

Use \( T_{^\circ\text{F}} = 1.8(T_{^\circ\text{C}}) + 32 \): \( 1.8×101 + 32 = 213.8 \)

Step7: Convert 75°F to °C

Use \( T_{^\circ\text{C}} = (T_{^\circ\text{F}} - 32)/1.8 \): \( (75 - 32)/1.8 ≈ 23.89 \)

Step8: Convert 64°F to K

First to °C: \( (64 - 32)/1.8 ≈ 17.78 \); then to K: \( 17.78 + 273.15 ≈ 290.93 \)

Step9: Convert 320 K to °F

First to °C: \( 320 - 273.15 = 46.85 \); then to °F: \( 1.8×46.85 + 32 ≈ 116.33 \)

Step10: Convert 36°F to K

First to °C: \( (36 - 32)/1.8 ≈ 2.22 \); then to K: \( 2.22 + 273.15 ≈ 275.37 \)

Step11: Convert 298 K to °F

First to °C: \( 298 - 273.15 = 24.85 \); then to °F: \( 1.8×24.85 + 32 ≈ 76.73 \)

Answer:

348.15
16.85
297.15
29.44
53.6
213.8
23.89
290.93
116.33
275.37
76.73