The air temperature decreases with increasing altitude above sea level. On a particular day the air temperature in is calculated from the formula:
where is the number of 100 m in altitude gain, and is rounded to the nearest whole number.
a i From the formula, what is the air temperature at sea level?

ii What is the change in temperature per 100 m altitude gain?

b Find the temperature for these places, rounding answers to the nearest whole number.
i Cabramurra, NSW, altitude 1462 m (Australia’s highest town)

ii Mt Cook summit, New Zealand, altitude 3754 m

c A mountaineer descends from the summit of Mt Everest, altitude 8850 m , to Everest Base Camp, altitude 5360 m . What is the change in the air temperature?

Ask by Stanley Fitzgerald. in Australia

Mar 25,2025

Question

The air temperature decreases with increasing altitude above sea level. On a particular day the air temperature in is calculated from the formula:
where is the number of 100 m in altitude gain, and is rounded to the nearest whole number.
a i From the formula, what is the air temperature at sea level?

ii What is the change in temperature per 100 m altitude gain?

b Find the temperature for these places, rounding answers to the nearest whole number.
i Cabramurra, NSW, altitude 1462 m (Australia’s highest town)

ii Mt Cook summit, New Zealand, altitude 3754 m

c A mountaineer descends from the summit of Mt Everest, altitude 8850 m , to Everest Base Camp, altitude 5360 m . What is the change in the air temperature?

Ask by Stanley Fitzgerald. in Australia

Mar 25,2025

UpStudy AI · Accepted Answer

**a i. Air temperature at sea level**

At sea level the altitude is 0 m. Since $$ n $$ represents the number of 100 m intervals and at sea level $$ n=0 $$, we substitute into the formula:

$$
T = 15 - 0.6(0) = 15\,^{\circ}\text{C}.
$$

**a ii. Change in temperature per 100 m altitude gain**

The formula is

$$
T = 15 - 0.6 n,
$$

so the coefficient $$-0.6$$ represents the change in temperature per 100 m altitude gain. That is, the temperature decreases by $$ 0.6\,^{\circ}\text{C} $$ for every 100 m increase in altitude.

---

**b. Temperature for specific locations**

*Note:* For each altitude, we first convert the altitude in meters to the number of 100 m intervals by dividing by 100 and rounding to the nearest whole number.

**b i. Cabramurra, NSW (altitude 1462 m)**

1. Calculate $$ n $$:
   $$
   n = \frac{1462}{100} = 14.62 \quad \text{(rounds to } 15\text{)}.
   $$
2. Substitute $$ n = 15 $$ into the formula:
   $$
   T = 15 - 0.6(15) = 15 - 9 = 6\,^{\circ}\text{C}.
   $$

**b ii. Mt Cook summit, New Zealand (altitude 3754 m)**

1. Calculate $$ n $$:
   $$
   n = \frac{3754}{100} = 37.54 \quad \text{(rounds to } 38\text{)}.
   $$
2. Substitute $$ n = 38 $$ into the formula:
   $$
   T = 15 - 0.6(38) = 15 - 22.8 = -7.8\,^{\circ}\text{C}.
   $$
3. Rounding to the nearest whole number gives:
   $$
   T \approx -8\,^{\circ}\text{C}.
   $$

---

**c. Temperature change during descent from Mt Everest summit to Base Camp**

For the summit of Mt Everest:
1. Altitude $$ = 8850 $$ m:
   $$
   n = \frac{8850}{100} = 88.5 \quad \text{(rounds to } 89\text{)}.
   $$
2. Temperature at the summit:
   $$
   T_{\text{summit}} = 15 - 0.6(89) = 15 - 53.4 = -38.4\,^{\circ}\text{C}.
   $$
   Rounding to the nearest whole number gives $$ T_{\text{summit}} \approx -38\,^{\circ}\text{C} $$.

For Everest Base Camp:
1. Altitude $$ = 5360 $$ m:
   $$
   n = \frac{5360}{100} = 53.6 \quad \text{(rounds to } 54\text{)}.
   $$
2. Temperature at Base Camp:
   $$
   T_{\text{base}} = 15 - 0.6(54) = 15 - 32.4 = -17.4\,^{\circ}\text{C}.
   $$
   Rounding to the nearest whole number gives $$ T_{\text{base}} \approx -17\,^{\circ}\text{C} $$.

**Change in temperature:**

$$
\Delta T = T_{\text{base}} - T_{\text{summit}} = (-17) - (-38) = 21\,^{\circ}\text{C}.
$$

Therefore, as the mountaineer descends from the summit to Base Camp, the air temperature increases by $$ 21\,^{\circ}\text{C} $$.
**a i. Air temperature at sea level:** $$ 15\,^{\circ}\text{C} $$ **a ii. Change in temperature per 100 m altitude gain:** $$ -0.6\,^{\circ}\text{C} $$ per 100 m **b i. Cabramurra, NSW (1462 m):** $$ 6\,^{\circ}\text{C} $$ **b ii. Mt Cook summit, New Zealand (3754 m):** $$ -8\,^{\circ}\text{C} $$ **c. Temperature change during descent from Mt Everest summit to Base Camp:** $$ 21\,^{\circ}\text{C} $$ increase

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